The Euler characteristic of hypersurfaces in space forms and its application to isoparametric hypersurfaces

Abstract

We revisit the Allendoerfer–Weil formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, taking time to re-prove it while demonstrating techniques of ([http://hdl.handle.net/10174/26893]) and then applying it to gain new understanding of isoparametric hypersurfaces.